Properties

Label 48.2.c
Level $48$
Weight $2$
Character orbit 48.c
Rep. character $\chi_{48}(47,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 48.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(48, [\chi])\).

Total New Old
Modular forms 14 2 12
Cusp forms 2 2 0
Eisenstein series 12 0 12

Trace form

\( 2q - 6q^{9} + O(q^{10}) \) \( 2q - 6q^{9} - 4q^{13} + 12q^{21} + 10q^{25} - 20q^{37} - 10q^{49} - 12q^{57} + 28q^{61} + 20q^{73} + 18q^{81} - 36q^{93} - 28q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
48.2.c.a \(2\) \(0.383\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{3}+2\zeta_{6}q^{7}-3q^{9}-2q^{13}+\cdots\)